History

The history of European logic is typically traced back to ancient Greece and the writings of Aristotle (384–322 BC).[1][4] Logic was established as a formal discipline by Aristotle, who gave it a fundamental place in philosophy. The study of logic was part of the classical trivium, which also included grammar and rhetoric. His formulation of so-called Aristotelian logic was the dominant form of formal logic in Europe until the late 18th to early 19th centuries.

In the Islamic world, Logic was further extended by Al-Farabi who categorized it into two separate groups (idea and proof). Later, Avicenna revived the study of logic and developed relationship between temporalis and the implication. Averroes defined logic as "the tool for distinguishing between the true and the false";[5]Richard Whately, '"the Science, as well as the Art, of reasoning"; and Frege, "the science of the most general laws of truth".

The late 18th to early 19th centuries saw the development of symbolic logic and mathematical logic introduced new paradoxes and more powerful techniques to deal with them.

History of logic

Several ancient civilizations have employed intricate systems of reasoning and asked questions about logic or propounded logical paradoxes. In Indian logic, the Nasadiya Sukta of the Rigveda (RV 10.129) contains ontological speculation in terms of various logical divisions that were later recast formally as the four circles of catuṣkoṭi: "A", "not A", "Neither A or not A", and "Both not A and not not A".[6] The Chinese logical philosopher Gongsun Long (ca. 325–250 BC) proposed the paradox "One and one cannot become two, since neither becomes two."[7] Also, the Chinese School of Names is recorded as having examined logical puzzles such as "A White Horse is not a Horse" as early as the fifth century BCE.[8] In China, the tradition of scholarly investigation into logic, however, was repressed by the Qin dynasty following the legalist philosophy of Han Feizi. The earliest sustained Greek work on the subject of logic is that of Aristotle.[9]Aristotelian logic became widely accepted in science and mathematics and remained in wide use in Europe until the early 19th century.

Islamic logic contributed to the development of modern logic, which included the development of "Avicennian logic"[10] as an alternative to Aristotelian logic. Avicenna's system of logic was responsible for the introduction of hypothetical syllogism,[11]temporalmodal logic,[12][13] and inductive logic.[14][15] It later had a significant influence on European logic during the Renaissance. In Europe during the later medieval period, major efforts were made to show that Aristotle's ideas were compatible with Christian faith. During the later period of the Middle Ages, logic became a main focus of philosophers, who would engage in critical logical analyses of philosophical arguments.

In India, innovations in the scholastic school, called Nyaya, continued from ancient times into the early 18th century with the Navya-Nyaya school. By the 16th century, it developed theories resembling modern logic, such as Gottlob Frege's "distinction between sense and reference of proper names" and his "definition of number," as well as the theory of "restrictive conditions for universals" anticipating some of the developments in modern set theory.[16] Since 1824, Indian logic attracted the attention of many Western scholars, and has had an influence on important 19th-century logicians such as Charles Babbage, Augustus De Morgan, and George Boole.[17] In the 20th century, Western philosophers like Stanislaw Schayer and Klaus Glashoff have explored Indian logic more extensively.

The development of logic since Frege, Russell and Wittgenstein had a profound influence on the practice of philosophy and the perceived nature of philosophical problems (see Analytic philosophy), and Philosophy of mathematics. Logic, especially sentential logic, is implemented in computer logic circuits and is fundamental to computer science. Logic is commonly taught by university philosophy departments often as a compulsory discipline.

↑The four Catuṣkoṭi logical divisions are formally very close to the four opposed propositions of the Greek tetralemma, which in turn are analogous to the four truth values of modern relevance logic Cf. Belnap (1977); Jayatilleke, K. N., (1967, The logic of four alternatives, in Philosophy East and West, University of Hawaii Press).

↑Kisor Kumar Chakrabarti (June 1976), "Some Comparisons Between Frege's Logic and Navya-Nyaya Logic", Philosophy and Phenomenological Research (International Phenomenological Society) 36 (4): 554–563, http://www.jstor.org/stable/2106873, "This paper consists of three parts. The first part deals with Frege's distinction between sense and reference of proper names and a similar distinction in Navya-Nyaya logic. In the second part we have compared Frege's definition of number to the Navya-Nyaya definition of number. In the third part we have shown how the study of the so-called 'restrictive conditions for universals' in Navya-Nyaya logic anticipated some of the developments of modern set theory."